The dimensional formula of electric intensity is

Options

A. `[M^(1)L^(1)T^(3)A^(-1)]`
B. `[ML^(-1)T^(-3)A^(1)]`
C. `[M^(1)L^(1)T^(-3)A^(-1)]`
D. `[M^(1)L^(2)T^(1)A^(1)]`

Explanation

To find the dimensional formula of electric intensity (E), we start with its definition. Electric intensity is defined as the force (F) experienced by a unit charge (Q). The formula can be expressed as:

\[ E = \frac{F}{Q} \]

### Step 1: Identify the dimensional formula of force (F)
The dimensional formula of force (F) is derived from Newton's second law, which states that force is the product of mass and acceleration. The dimensional formula for mass (M) is \( [M] \), and for acceleration (A), it is given by:

\[ A = \frac{\text{change in velocity}}{\text{time}} = \frac{L/T}{T} = \frac{L}{T^2} \]

Thus, the dimensional formula for force (F) is:

\[ F = M \cdot A = M \cdot \frac{L}{T^2} = MLT^{-2} \]

### Step 2: Identify the dimensional formula of electric charge (Q)
The dimensional formula for electric charge (Q) is represented as:

\[ [Q] = [A][T] \]

where \( [A] \) is the dimensional formula for electric current and \( [T] \) is for time. Therefore, the dimensional formula for charge is:

\[ [Q] = AT \]

### Step 3: Substitute the dimensional formulas into the electric intensity formula
Now we substitute the dimensional formulas of force and charge into the formula for electric intensity:

\[ E = \frac{F}{Q} = \frac{MLT^{-2}}{AT} \]

### Step 4: Simplify the expression
When we simplify the expression, we get:

\[ E = \frac{MLT^{-2}}{AT} = \frac{M}{A} \cdot \frac{L}{T^2} = M^1 L^1 A^{-1} T^{-2} \]

### Step 5: Rearrange the dimensional formula
To express the dimensional formula in a standard order (M, L, T, A), we can write:

\[ E = M^1 L^1 T^{-2} A^{-1} \]

### Final Result
Thus, the dimensional formula of electric intensity is:

\[ [E] = M^1 L^1 T^{-2} A^{-1} \]

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